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arXiv · 2604.14715

Uniform volume estimates and maximal functions on generalized Heisenberg-type groups

Cheng Bi·Hong-Quan Li
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Abstract

On generalized Heisenberg-type groups $\mathbb{G}(2n,m,\mathbb{U},\mathbb{W})$, we give uniform volume estimates for the ball defined by a large class of Carnot-Carath\'{e}odory distances, and establish weak (1, 1) $O(C^m \, n)$-estimates for associated centered Hardy-Littlewood maximal functions, extending the results in \cite{BLZ25}. As a by-product, we establish uniformly volume doubling property on Heisenberg groups for a class of left-invariant Riemannian metrics.

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Cheng Bi, Hong-Quan Li. 2026-04-16. Uniform volume estimates and maximal functions on generalized Heisenberg-type groups. https://arxiv.org/abs/2604.14715

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